

A104148


Difference between n^3 and largest m less than n^3, where m > 0 is either a prime or a square.


1



1, 2, 3, 4, 5, 6, 3, 2, 3, 4, 5, 18, 3, 2, 3, 4, 5, 2, 7, 4, 9, 4, 17, 6, 3, 2, 9, 10, 7, 2, 7, 4, 3, 12, 7, 2, 3, 38, 3, 4, 11, 14, 25, 4, 9, 10, 5, 6, 9, 4, 5, 4, 7, 12, 15, 4, 9, 22, 17, 38, 7, 4, 5, 16, 5, 2, 9, 28, 11, 28, 17, 14, 3, 28, 9, 4, 5, 12, 3, 58, 5
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OFFSET

2,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..1000


FORMULA

a(n) < 2n^(3/2)  1. Conjecturally a(n) << log^2 n.  Charles R Greathouse IV, Jun 03 2013


EXAMPLE

a(5) = 4 because largest square less than 5^3 is 121 and 125  121 = 4.


MATHEMATICA

lst = {}; Do[k = n^3; a = NextPrime[k, 1]; b = Floor@Sqrt[k  1]^2; AppendTo[lst, k  Max[a, b]], {n, 2, 82}]; lst (* Arkadiusz Wesolowski, Jun 03 2013 *)


PROG

(MAGMA) [n^3Maximum(Isqrt(n^31)^2, PreviousPrime(n^3)): n in [2..100]]; // Bruno Berselli, Jun 03 2013
(PARI) a(n)=n^3max(sqrtint(n^31)^2, precprime(n^3)) \\ Charles R Greathouse IV, Jun 03 2013


CROSSREFS

Sequence in context: A203580 A043266 A082120 * A286450 A245344 A323074
Adjacent sequences: A104145 A104146 A104147 * A104149 A104150 A104151


KEYWORD

nonn,easy


AUTHOR

Giovanni Teofilatto, Mar 08 2005


EXTENSIONS

Offset corrected by Michel Marcus, Jun 03 2013
Edited, corrected and extended by Arkadiusz Wesolowski, Jun 03 2013


STATUS

approved



